mrjones wrote:I looked at the talk page for the Wikipedia article, and it seems that the article (and Zach's comic) is basically incorrect and the point of the game is NOT to show that "rational choices can lead to irrational behaviour" (which is, as far as i understand, nonsense), but rather to argue that people will typically not behave rationally in this kind of situation.

Quoting your Wikipedia article directly:

The dollar auction is a non-zero sum sequential game designed by economist Martin Shubik to illustrate a paradox brought about by traditional rational choice theory in which players with perfect information in the game are compelled to make an ultimately irrational decision based completely on a sequence of rational choices made throughout the game.

You're both right (though derp is more right in that that's what the thought experiment was designed to illustrate). Decisions made during the game are not rational, in the classical sense.When playing alone the rational choice is to bid minimum. (this much is true)When playing against a non-zero quantity of completely rational opponents the rational choice is to bid 99 cents. (this is the usual decision pattern, and I'm going to show it's bullshit)When playing against even a little irrational opponent (such as someone who generally follows only profit, but also has a desire to "win") the rational move is not to play. Your risk is 99 cents, your reward is 1 cent, thus (even assuming you have much larger stocks of money, and assign the same value to a cent lost as a cent gained) even a collections of opponents who are together 1.1% likely to outdo your 99 cent bid will statistically make you lose money. It's ultimately impossible to know all your opponents to such a degree without expending significant resources (likely to exceed your 1 cent gain). Thus the rational move is to never play Dollar Auction.

Liger wrote:The economic definition of rationality is that "a choice is rational if making said choice will result in more profit than not making the choice."

Seems like naive/strawman rationality to me. A truly rational agent should be able to model other rational agents and realize that the bidding game is a losing proposition and just not participate.

The issue here being, of course, that if you're modelling other rational agents, and have come to the conclusion that the rational thing to do is not to bid, then they should also (being just as rational, with the same information) choose not to bid, so they won't get into a bidding war with you, which means that you should bid, but they can come to that conclusion too, which means you shouldn't bid, which means you should bid which means...Bidding over a dollar might be irrational, but bidding at all can't be. Though I can't be bothered to solve the game fully right now, so I can't be sure how you should bid. At a guess, it would probably depend how much you had available.

Sure, and if you do that a thousand times and it never fails (it will, at least sometimes) you get $10 for your efforts and risk. Still strengthens the point that the most rational person will avoid it altogether. Unless you adjust the values such that the next lowest amount you can wager is actually a significant amount of money, it's not worth it.

mrjones wrote:Before accepting the Wikipedia article as a source, at least look at the talk page. The top post there in particular.

Maybe you should look at the article that the poster on the talk page linked as their reference? O'Neill makes it clear that while there are completely rational ways to play the dollar auction, it is only possible in an 'ideal' situation, which generally doesn't exist.* He details a variety of reasons why the ideal situation doesn't exist and how they apply to international conflict.** A major one being that there has to be explicit assumptions as to how much each player has to bid, as it has a serious impact. O'Neill's rational solutions rely on other things that don't really happen in the real world, like unlimited foresight ("look ahead"). He also includes irrational issues, like the desire to win for the sake of winning. His only real critique of the dollar auction that I read is that it is basically entrapping in a non-ideal situation.

There are also plenty of examples of experiments where the dollar auction has actually been carried out and have backed Shubik's prediction. There seems to be a misinterpretation. Shubik only claimed that the individual actions (bids) were rational, not that the total behavior was rational. That was the point. O'Neill is mostly just expanding on it to show what factors in a non-ideal (also known as real world) situation cause the total behavior to be irrational in regards to international conflict.*** I assume so the downward spiral predicted by the dollar auction could be preempted in serious situations of diplomacy gone awry.

*In the same way that you can't assume perfect, rigid-body spheres in a vacuum when doing projectile motion. In the real world you can't ignore air resistance, deformation, and irregularities.**It being a paper in the Journal of Conflict Resolution. Context matters.***Again, context matters.

Kaharz wrote:I don't need a title. I have no avatar or tagline either. I am unique in my lack of personal identifiers.

mrjones wrote:Before accepting the Wikipedia article as a source, at least look at the talk page. The top post there in particular.

Maybe you should look at the article that the poster on the talk page linked as their reference? O'Neill makes it clear that while there are completely rational ways to play the dollar auction, it is only possible in an 'ideal' situation, which generally doesn't exist.* He details a variety of reasons why the ideal situation doesn't exist and how they apply to international conflict.** A major one being that there has to be explicit assumptions as to how much each player has to bid, as it has a serious impact. O'Neill's rational solutions rely on other things that don't really happen in the real world, like unlimited foresight ("look ahead"). He also includes irrational issues, like the desire to win for the sake of winning. His only real critique of the dollar auction that I read is that it is basically entrapping in a non-ideal situation.

There are also plenty of examples of experiments where the dollar auction has actually been carried out and have backed Shubik's prediction. There seems to be a misinterpretation. Shubik only claimed that the individual actions (bids) were rational, not that the total behavior was rational. That was the point. O'Neill is mostly just expanding on it to show what factors in a non-ideal (also known as real world) situation cause the total behavior to be irrational in regards to international conflict.*** I assume so the downward spiral predicted by the dollar auction could be preempted in serious situations of diplomacy gone awry.

*In the same way that you can't assume perfect, rigid-body spheres in a vacuum when doing projectile motion. In the real world you can't ignore air resistance, deformation, and irregularities.**It being a paper in the Journal of Conflict Resolution. Context matters.***Again, context matters.

The applications to real world conflicts are irrelevant to the question. It doesn't matter, for example, that perfectly rational people don't exist in the real world, or that the dollar auction is not a perfect model of, e.g., an arms race. The claim in the comic was that 'rational choices can lead to irrational behavior'. That is false and self-contradictory. Rationality can be defined precisely, and when the rules of the game are defined precisely you can work out how a rational being would act (as is done in the article).

Verbatim from article: "In this article I calculate the rational strategies for the two players and show that there would be no escalation of bids if both acted rationally."

Btw, you don't need 'unlimited foresight' to play perfectly. If you know that your opponent is rational, you can solve the game just like it's done in the article.

You mention experiments. They are irrelevant as the question is not how real people will play this game (answer: irrationally), but how the game would be played rationally.

mrjones wrote:Before accepting the Wikipedia article as a source, at least look at the talk page. The top post there in particular.

The claim in the comic was that 'rational choices can lead to irrational behavior' ... Rationality can be defined precisely, and when the rules of the game are defined precisely you can work out how a rational being would act (as is done in the article).

[/quote]If you take that view, then the claim becomes a contradiction in terms (like "four sided triangle",) rather then merely false, since in context of Game Theory, "behavior" and (series of) "choices" are synonyms. Your defeat of strawman arguments, while valiant, brings no new insight.It's clear from context, that we can only assume one player to be rational (even that is a bit of a stretch, given their depicted actions, but let's take it at face value) while the rest are the flawed human animal we know and love. And that it leads to a string of decisions that, in hindsight, appear irrational.

mrjones wrote:Before accepting the Wikipedia article as a source, at least look at the talk page. The top post there in particular.

The claim in the comic was that 'rational choices can lead to irrational behavior' ... Rationality can be defined precisely, and when the rules of the game are defined precisely you can work out how a rational being would act (as is done in the article).

If you take that view, then the claim becomes a contradiction in terms (like "four sided triangle",) rather then merely false, since in context of Game Theory, "behavior" and (series of) "choices" are synonyms. Your defeat of strawman arguments, while valiant, brings no new insight.It's clear from context, that we can only assume one player to be rational (even that is a bit of a stretch, given their depicted actions, but let's take it at face value) while the rest are the flawed human animal we know and love. And that it leads to a string of decisions that, in hindsight, appear irrational.[/quote]

Yes, like I said the claim is self-contradictory. But, no, the escalation of bids is not not rational in any scenario.

Imagine you are a rational player faced with a player whom you cannot assume to be rational. The 'correct strategy' (assuming a rational opponent) would be to bid 60 cents, at which point the auction would end. However, you don't know that your opponent is rational, so are you being rational in bidding 60 cents? Probably not. In any case, if you do bid, and your opponent raises, clearly it is now foolish (irrational) to keep escalating. You have no reason to believe that your opponent won't keep raising. After the bids have escalated far enough, claiming that continued escalation is rational (This claim IS MADE in the comic and on the Wikipedia page [but not by Shubik or O'Neill]. This is not a strawman argument) is completely ridiculous.

mrjones wrote:Imagine you are a rational player faced with a player whom you cannot assume to be rational. The 'correct strategy' (assuming a rational opponent) would be to bid 60 cents.

It would be, but that's an illegal play. Shubik's Dollar Auction actually works more like a poker game, you can either "raise 5 cents" or "fold" (you can't "check" however, nor does raising increase the ante). That however doesn't change the fact that a game between rational opponents, the winning move is, in the immortal words of Joshua the NORAD Computer, not to play.

@guest. The Wikipedia article does not support your view (I think they'd mention if it was a poker game ). You can't just make up rules on the spot to win arguments. This isn't Calvinball Fake edit: in fact, here: http://www.heretical.com/pound/dollar.html1. (As in any auction) the dollar bill goes to the highest bidder, who pays whatever the high bid was. Each new bid has to be higher than the current high bid, and the game ends when there is no new bid within a specified time limit.2. (Unlike at Sotheby’s!) the second-highest bidder also has to pay the amount of his last bid – and gets nothing in return. You really don’t want to be the second-highest bidder.(In case you didn't catch that- it's from an actual, published, book by someone who actually knows something)